Question

find the function, f(x)=3x+4 and g(x)=x^2-2 find(f * g)(-2)


A)-14
B)10
C)-22
D)2

Answer 1

First, we need to find f * g, which means we need to find the function that results from multiplying f(x) by g(x).

f(x) = 3x + 4
g(x) = x^2 - 2

(f * g)(x) = (3x + 4)(x^2 - 2)
(f * g)(x) = 3x(x^2 - 2) + 4(x^2 - 2)
(f * g)(x) = 3x^3 - 6x + 4x^2 -8
(f * g)(x) = 3x^3 + 4x^2 - 6x - 8

Now, we need to find (f * g)(-2).

(f * g)(-2) = 3(-2)^3 + 4(-2)^2 - 6(-2) - 8
(f * g)(-2) = 3(-8) + 4(4) + 12 - 8
(f * g)(-2) = -24 + 16 + 12 - 8
(f * g)(-2) = -8 + 12 - 8
(f * g)(-2) = 4 - 8
(f * g)(-2) = -4

Therefore, (f * g)(-2) = -4, which corresponds to answer choice D) 2.